Gamora and Peter meet each other on Xandar outside the Broker's shop. However, Gamora tried killing him while trying to stealing the Orb from Peter.
Both of them hide their feelings for each other, but Peter is more open of his relationship to Gamora over her.
They are all on first name terms with each other.
In the comics, Peter Quill was briefly "engaged" to Kitty Pryde, a mutant who is known for her ability to phase through solid objects like walls, and doors. However, she does not appear in any of the MCU films, due to her film rights being owned by 20th Century Fox when the Guardians films first went into production. At one point, Kitty even took on the " Star-Lord" mantle when Quill was forced to rule Spartax as its "president".
When asked about Peter and Gamora's relationship status by the end of Guardians of the Galaxy Vol.2, director James Gunn stated that the two have since became a canon couple.